 
(* ::Section:: *)
(* Kummer *)
(* ::Text:: *)
(*Kummer[i][exp] applies Kummer relation number i (i =1, ... 24, 94,95,96) to all Hypergeometric2F1 in exp. i = 94 corresponds to eq. 9.131.2, i = 95 to eq. 9.132.1 and i = 96 to eq. 9.132.2 in Gradsteyn & Ryzhik..*)


(* ::Subsection:: *)
(* See also *)
(* ::Text:: *)
(*HypergeometricAC.*)



(* ::Subsection:: *)
(* Examples *)



Hypergeometric2F1[a,b,c,z]==Kummer[2][Hypergeometric2F1[a,b,c,z]]

Hypergeometric2F1[a,b,c,z]==Kummer[3][Hypergeometric2F1[a,b,c,z]]

Hypergeometric2F1[a,b,c,z]==Kummer[4][Hypergeometric2F1[a,b,c,z]]

Hypergeometric2F1[a,b,c,1-z]==Kummer[6][Hypergeometric2F1[a,b,c,1-z]]

Hypergeometric2F1[a,b,a+b+1-c,1-z]==Kummer[6][Hypergeometric2F1[a,b,a+b+1-c,1-z]]

Hypergeometric2F1[a,b,c,1-z]==Kummer[7][Hypergeometric2F1[a,b,c,1-z]]

Hypergeometric2F1[a,b,a+b+1-c,1-z]==Kummer[7][Hypergeometric2F1[a,b,a+b+1-c,1-z]]

Hypergeometric2F1[a,b,c,1-z]==Kummer[8][Hypergeometric2F1[a,b,c,1-z]]

Hypergeometric2F1[a,b,a+b+1-c,1-z]==Kummer[8][Hypergeometric2F1[a,b,a+b+1-c,1-z]]

Hypergeometric2F1[a,b,c,z^(-1)]==Kummer[10][Hypergeometric2F1[a,b,c,z^(-1)]]

Hypergeometric2F1[a,a+1-c,a+1-b,z^(-1)]==Kummer[10][Hypergeometric2F1[a,a+1-c,a+1-b,z^(-1)]]

Hypergeometric2F1[a,b,c,z^(-1)]==Kummer[11][Hypergeometric2F1[a,b,c,z^(-1)]]

Hypergeometric2F1[a,a+1-c,a+1-b,z^(-1)]==Kummer[11][Hypergeometric2F1[a,a+1-c,a+1-b,z^(-1)]]

Hypergeometric2F1[a,b,c,z^(-1)]==Kummer[12][Hypergeometric2F1[a,b,c,z^(-1)]]

Hypergeometric2F1[a,a+1-c,a+1-b,z^(-1)]==Kummer[12][Hypergeometric2F1[a,a+1-c,a+1-b,z^(-1)]]

Hypergeometric2F1[a,b,c,z^(-1)]==Kummer[14][Hypergeometric2F1[a,b,c,z^(-1)]]

Hypergeometric2F1[b+1-c,b,b+1-a,z^(-1)]==Kummer[14][Hypergeometric2F1[b+1-c,b,b+1-a,z^(-1)]]

Hypergeometric2F1[a,b,c,z^(-1)]==Kummer[15][Hypergeometric2F1[a,b,c,z^(-1)]]

Hypergeometric2F1[b+1-c,b,b+1-a,z^(-1)]==Kummer[15][Hypergeometric2F1[b+1-c,b,b+1-a,z^(-1)]]

Hypergeometric2F1[a,b,c,z^(-1)]==Kummer[16][Hypergeometric2F1[a,b,c,z^(-1)]]

Hypergeometric2F1[b+1-c,b,b+1-a,z^(-1)]==Kummer[16][Hypergeometric2F1[b+1-c,b,b+1-a,z^(-1)]]

Hypergeometric2F1[a+1-c,b+1-c,2-c,z]==Kummer[18][Hypergeometric2F1[a+1-c,b+1-c,2-c,z]]

Hypergeometric2F1[a,b,c,z]==Kummer[18][Hypergeometric2F1[a,b,c,z]]

Hypergeometric2F1[a+1-c,b+1-c,2-c,z]==Kummer[19][Hypergeometric2F1[a+1-c,b+1-c,2-c,z]]

Hypergeometric2F1[a,b,c,z]==Kummer[19][Hypergeometric2F1[a,b,c,z]]

Hypergeometric2F1[a+1-c,b+1-c,2-c,z]==Kummer[20][Hypergeometric2F1[a+1-c,b+1-c,2-c,z]]

Hypergeometric2F1[a,b,c,z]==Kummer[20][Hypergeometric2F1[a,b,c,z]]

Hypergeometric2F1[c-a,c-b,c+1-a-b,1-z]==Kummer[22][Hypergeometric2F1[c-a,c-b,c+1-a-b,1-z]]

Hypergeometric2F1[a,b,c,1-z]==Kummer[22][Hypergeometric2F1[a,b,c,1-z]]

Hypergeometric2F1[c-a,c-b,c+1-a-b,1-z]==Kummer[23][Hypergeometric2F1[c-a,c-b,c+1-a-b,1-z]]

Hypergeometric2F1[a,b,c,1-z]==Kummer[23][Hypergeometric2F1[a,b,c,1-z]]

Hypergeometric2F1[c-a,c-b,c+1-a-b,1-z]==Kummer[24][Hypergeometric2F1[c-a,c-b,c+1-a-b,1-z]]

Hypergeometric2F1[a,b,c,1-z]==Kummer[24][Hypergeometric2F1[a,b,c,1-z]]

Hypergeometric2F1[a,b,c,z]==Kummer[94][Hypergeometric2F1[a,b,c,z]]

Hypergeometric2F1[a,b,c,z]==Kummer[95][Hypergeometric2F1[a,b,c,z]]

Hypergeometric2F1[a,b,c,z]==Kummer[96][Hypergeometric2F1[a,b,c,z]]
